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Definition

For S⊂XS \subset X a subset of a topological spaceXX, a, interior point of SS is a point x∈Sx \in S which has a neighbourhood in XX that is contained in SS. The union of all interior points is the interiorS∘S^\circ of SS.

In general, we have S∘⊆SS^\circ \subseteq S. SS is open if and only if S∘=SS^\circ = S.